So, the cable that causes the light to go out has a short. Since it is the antenna coax it's possible the short is at the head or inside the antenna. You need to disconnect the coax from the head of the antenna. If the light now comes on and stays on then you need to replace the antenna head. If the light still does not come on you likely just have a bad connector on one end of the coax (usually outside). Cut the coax back until you see clean shiny center wire and shielding and put on a new F-connector. I suggest using compression fittings which are available at Lowes and Home Depot along with the compression tool. Also, stop by your local auto parts store and pick up some di-electric grease in a small tube. Once you make a new connection outside (not necessary inside) squeeze a bit of grease in that F-connector before screwing it back onto the head. You should be in pretty good shape after that gets done.